Chapter 4 - Answer - Cost accounting PDF

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COST ACCOUNTING AND CONTROL – Solutions ManualCHAPTER 4 COST-VOLUME-PROFIT RELATIONSHIPI. Answers to Questions The total “contribution margin” is the excess of total revenue over total variable costs. The unit contribution margin is the excess of the unit price over the unit variable costs. Total co...

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COST ACCOUNTING AND CONTROL – Solutions Manual CHAPTER 4 COST-VOLUME-PROFIT RELATIONSHIP I.

Answers to Questions 1.

The total “contribution margin” is the excess of total revenue over total variable costs. The unit contribution margin is the excess of the unit price over the unit variable costs.

2.

Total contribution margin: Selling price - manufacturing variable costs expensed - nonmanufacturing variable costs expensed = Total contribution margin. Gross margin: Selling price - variable manufacturing costs expensed - fixed manufacturing costs expensed = Gross margin.

3.

A company operating at “break-even” is probably not covering costs which are not recorded in the accounting records. An example of such a cost is the opportunity cost of owner-invested capital. In some small businesses, ownermanagers may not take a salary as large as the opportunity cost of forgone alternative employment. Hence, the opportunity cost of owner labor may be excluded.

4.

In the short-run, without considering asset replacement, net operating cash flows would be expected to exceed net income, because the latter includes depreciation expense, while the former does not. Thus, the cash basis breakeven would be lower than the accrual break-even if asset replacement is ignored. However, if asset replacement costs are taken into account, (i.e., on a “cradle to grave” basis), the long-run net cash flows equal long-run accrual net income, and the long-run break-even points are the same.

5.

Both unit price and unit variable costs are expressed on a per product basis, as:  = (P1 - V1) X1 + (P2 - V2) X2 +  + (Pn - Vn) Xn - F, for all products 1 to n where:  P V X F

6.

= = = = =

operating profit, average unit selling price, average unit variable cost, quantity of units, total fixed costs for the period.

If the relative proportions of products (i.e., the product “mix”) is not held constant, products may be substituted for each other. Thus, there may be almost an infinite number of ways to achieve a target operating profit. As shown from the multiple product profit equation, there are several unknowns for one equation:

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 = (P1 - V1) X1 + (P2 - V2) X2 +  + (Pn - Vn) Xn - F, for all products 1 to n. 7.

A constant product mix is assumed to simplify the analysis. Otherwise, there may be no unique solution.

8.

Operating leverage measures the impact on net operating income of a given percentage change in sales. The degree of operating leverage at a given level of sales is computed by dividing the contribution margin at that level of sales by the net operating income.

9.

Three approaches to break-even analysis are (a) the equation method, (b) the contribution margin method, and (c) the graphical method. In the equation method, the equation is: Sales = Variable expenses + Fixed expenses + Profits, where profits are zero at the break-even point. The equation is solved to determine the break-even point in units or peso sales.

10. The margin of safety is the excess of budgeted (or actual) sales over the breakeven volume of sales. It states the amount by which sales can drop before losses begin to be incurred. 11. The sales mix is the relative proportions in which a company’s products are sold. The usual assumption in cost-volume-profit analysis is that the sales mix will not change. 12. A higher break-even point and a lower net operating income could result if the sales mix shifted from high contribution margin products to low contribution margin products. Such a shift would cause the average contribution margin ratio in the company to decline, resulting in less total contribution margin for a given amount of sales. Thus, net operating income would decline. With a lower contribution margin ratio, the break-even point would be higher since it would require more sales to cover the same amount of fixed costs. 13. The contribution margin (CM) ratio is the ratio of the total contribution margin to total sales revenue. It can be used in a variety of ways. For example, the change in total contribution margin from a given change in total sales revenue can be estimated by multiplying the change in total sales revenue by the CM ratio. If fixed costs do not change, then a peso increase in contribution margin will result in a peso increase in net operating income. The CM ratio can also be used in break-even analysis. Therefore, knowledge of a product’s CM ratio is extremely helpful in forecasting contribution margin and net operating income. 14. Incremental analysis focuses on the changes in revenues and costs that will result from a particular action. 15. All other things equal, Company B, with its higher fixed costs and lower variable costs, will have a higher contribution margin ratio than Company A. Therefore, it will tend to realize a larger increase in contribution margin and in profits when sales increase.

4-2

16. (a) If the selling price decreased, then the total revenue line would rise less steeply, and the break-even point would occur at a higher unit volume. (b) If the fixed cost increased, then both the fixed cost line and the total cost line would shift upward and the break-even point would occur at a higher unit volume. (c) If the variable cost increased, then the total cost line would rise more steeply and the break-even point would occur at a higher unit volume. II. Answers to Exercises Exercise 1 (Contribution Format Income Statement) Requirement 1 Total Per Unit Sales (30,000 units × 1.15 = 34,500 units)........................................................................... P172,500 P5.00 Less variable expenses.......................................................................................................... 103,500 3.00 Contribution margin.............................................................................................................. 69,000 P2.00 Less fixed expenses............................................................................................................... 50,000 Net operating income............................................................................................................ P 19,000 Requirement 2 Sales (30,000 units × 1.20 = 36,000 units)........................................................................... P162,000 P4.50 Less variable expenses.......................................................................................................... 108,000 3.00 Contribution margin.............................................................................................................. 54,000 P1.50 Less fixed expenses............................................................................................................... 50,000 Net operating income............................................................................................................ P 4,000 Requirement 3 Sales (30,000 units × 0.95 = 28,500 units)........................................................................... P156,750 P5.50 Less variable expenses.......................................................................................................... 85,500 3.00 Contribution margin.............................................................................................................. 71,250 P2.50 Less fixed expenses (P50,000 + P10,000)............................................................................ 60,000 Net operating income............................................................................................................ P 11,250

Requirement 4 Sales (30,000 units × 0.90 = 27,000 units)........................................................................... P151,200 P5.60 Less variable expenses.......................................................................................................... 86,400 3.20 Contribution margin.............................................................................................................. 64,800 P2.40 Less fixed expenses............................................................................................................... 50,000 Net operating income............................................................................................................ P 14,800 Exercise 2 (Break-even Analysis and CVP Graphing) 4-3

Requirement 1 The contribution margin per person would be: Price per ticket....................................................................................................................... P30 Less variable expenses: Dinner................................................................................................................................ P7 Favors and program........................................................................................................... 3 10 Contribution margin per person............................................................................................ P20 The fixed expenses of the Extravaganza total P8,000; therefore, the break-even point would be computed as follows: Sales

= Variable expenses + Fixed expense + Profits

P30Q P20Q Q Q

= = = =

P10Q + P8,000 + P0 P8,000 P8,000 ÷ P20 per person 400 persons; or, at P30 per person, P12,000

Alternative solution: Break-even point in unit sales

=

Fixed expenses Unit contribution margin

=

P8,000 P20 per person

400 persons = or, at P30 per person, P12,000. Requirement 2 Variable cost per person (P7 + P3)........................................................................................ P10 Fixed cost per person (P8,000 ÷ 250 persons)...................................................................... 32 Ticket price per person to break even................................................................................... P42 Requirement 3 Cost-volume-profit graph:

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P22,000 P20,000 P18,000 Total Sales

P16,000 Break-even point: 400 persons, or P12,000 in sales

Pesos

P14,000 P12,000 P10,000

Total Expenses Fixed Expenses

P8,000 P6,000 P4,000 P2,000 P0 0

100

200

300

400

500

Number of Persons

Exercise 3 (Break-even and Target Profit Analysis) Requirement 1 Sales P900Q P270Q Q Q

= = = = =

Variable expenses + Fixed expenses + Profits P630Q + P1,350,000 + P0 P1,350,000 P1,350,000 ÷ P270 per lantern 5,000 lanterns, or at P900 per lantern, P4,500,000 in sales

Alternative solution: Break-even point in unit sales

Fixed expenses Unit contribution margin

= = 4-5

=

P1,350,000 P270 per lantern 5,000 lanterns

600

or at P900 per lantern, P4,500,000 in sales Requirement 2 An increase in the variable expenses as a percentage of the selling price would result in a higher break-even point. The reason is that if variable expenses increase as a percentage of sales, then the contribution margin will decrease as a percentage of sales. A lower CM ratio would mean that more lanterns would have to be sold to generate enough contribution margin to cover the fixed costs.

Requirement 3 Present: 8,000 Lanterns Total Per Unit P7,200,000 P900 5,040,000 630 2,160,000 P270 1,350,000 P 810,000

Sales Less variable expenses Contribution margin Less fixed expenses Net operating income

Proposed: 10,000 Lanterns* Total Per Unit P8,100,000 P810 ** 6,300,000 630 1,800,000 P180 1,350,000 P 450,000

* 8,000 lanterns × 1.25 = 10,000 lanterns ** P900 per lantern × 0.9 = P810 per lantern As shown above, a 25% increase in volume is not enough to offset a 10% reduction in the selling price; thus, net operating income decreases. Requirement 4 Sales P810Q P180Q Q Q

= = = = =

Variable expenses + Fixed expenses + Profits P630Q + P1,350,000 + P720,000 P2,070,000 P2,070,000 ÷ P180 per lantern 11,500 lanterns

Alternative solution: Unit sales to attain target profit

=

Fixed expenses + Target profit Unit contribution margin

=

P1,350,000 + P720,000 P180 per lantern

=

11,500 lanterns 4-6

Exercise 4 (Operating Leverage) Requirement 1 Sales (30,000 doors).............................................................................................................. P18,000,000 P600 Less variable expenses.......................................................................................................... 12,600,000 420 Contribution margin.............................................................................................................. 5,400,000 P180 Less fixed expenses............................................................................................................... 4,500,000 Net operating income............................................................................................................ P 900,000 Degree of operating leverage

=

Contribution margin Net operating income

=

P5,400,000 P900,000

=

6

Requirement 2 a. b.

Sales of 37,500 doors represents an increase of 7,500 doors, or 25%, over present sales of 30,000 doors. Since the degree of operating leverage is 6, net operating income should increase by 6 times as much, or by 150% (6 × 25%). Expected total peso net operating income for the next year is: Present net operating income................................................................................................ P 900,000 Expected increase in net operating income next year (150% × P900,000)........................................................................................................... 1,350,000 Total expected net operating income.................................................................................... P2,250,000

Exercise 5 (Break-even Analysis; Target Profit; Margin of Safety) Requirement 1 Sales P40Q P12Q Q Q

= = = = =

Variable expenses + Fixed expenses + Profits P28Q + P150,000 + P0 P150,000 P150,000 ÷ P12 per unit 12,500 units, or at P40 per unit, P500,000

Alternatively: Break-even point in unit sales

Fixed expenses 4-7Unit contribution margin P150,000 = P12 per unit

=

=

12,500 units

or, at P40 per unit, P500,000. Requirement 2 The contribution margin at the break-even point is P150,000 since at that point it must equal the fixed expenses. Requirement 3 Unit sales to attain target profit

=

Fixed expenses + Target profit Unit contribution margin

=

P150,000 + P18,000 P12 per unit

=

14,000 units

Total Unit Sales (14,000 units × P40 per unit)....................................................................................... P560,000 P40 Less variable expenses (14,000 units × P28 per unit)............................................................................................ 392,000 28 Contribution margin (14,000 units × P12 per unit)............................................................................................ 168,000 P12 Less fixed expenses............................................................................................................... 150,000 Net operating income............................................................................................................ P 18,000 Requirement 4 Margin of safety in peso terms: Margin of safety in pesos =

Total sales =

–

P600,000

Break-even sales –

P500,000

Margin of safety in percentage terms: Margin of safety in pesos Margin of safety = Total sales percentage

= Requirement 5

P100,000 P600,000

= 16.7% (rounded) 4-8

=

P100,000

The CM ratio is 30%. Expected total contribution margin: P680,000 × 30%......................................................... P204,000 Present total contribution margin: P600,000 × 30%............................................................ 180,000 Increased contribution margin.............................................................................................. P 24,000 Alternative solution: P80,000 incremental sales × 30% CM ratio = P24,000 Since in this case the company’s fixed expenses will not change, monthly net operating income will increase by the amount of the increased contribution margin, P24,000. Exercise 6 (Changes in Variable Costs, Fixed Costs, Selling Price, and Volume) Requirement (1) The following table shows the effect of the proposed change in monthly advertising budget: Sales With Additional Current Advertising Sales Budget Difference Sales P225,000 P240,000 P15,000 Variable expenses............................... 135,000 144,000 9,000 Contribution margin........................... 90,000 96,000 6,000 Fixed expenses................................... 75,000 83,000 8,000 Net operating income......................... P 15,000 P 13,000 P(2,000) Assuming that there are no other important factors to be considered, the increase in the advertising budget should not be approved since it would lead to a decrease in net operating income of P2,000. Alternative Solution 1 Expected total contribution margin: P240,000 × 40% CM ratio..................................................... Present total contribution margin: P225,000 × 40% CM ratio..................................................... Incremental contribution margin............................................... Change in fixed expenses: Less incremental advertising expense................................... Change in net operating income................................................

P96,000 90,000 6,000 8,000 P(2,000)

Alternative Solution 2 Incremental contribution margin: P15,000 × 40% CM ratio...................................................... 4-9

P 6,000

Less incremental advertising expense....................................... Change in net operating income................................................

8,000 P(2,000)

Requirement (2) The P3 increase in variable costs will cause the unit contribution margin to decrease from P30 to P27 with the following impact on net operating income: Expected total contribution margin with the higher-quality components: 3,450 units × P27 per unit........................................................................... P93,150 Present total contribution margin: 3,000 units × P30 per unit........................................................................... 90,000 Change in total contribution margin............................................................... P 3,150 Assuming no change in fixed costs and all other factors remain the same, the higher-quality components should be used. Exercise 7 (Degree of Operating Leverage) Requirement (1) The company’s degree of operating leverage would be computed as follows: Contribution margin......................................... ÷ Net operating income.................................... Degree of operating leverage........................... Requirement (2)

P36,000 P12,000 3.0

A 10% increase in sales should result in a 30% increase in net operating income, computed as follows: Degree of operating leverage..................................................................................... 3.0 × Percent increase in sales......................................................................................... 10% Estimated percent increase in net operating income................................................. 30% Requirement (3) The new income statement reflecting the c...